1
JEE Main 2021 (Online) 27th August Evening Shift
Numerical
+4
-1
Let A (sec$$\theta$$, 2tan$$\theta$$) and B (sec$$\phi$$, 2tan$$\phi$$), where $$\theta$$ + $$\phi$$ = $$\pi$$/2, be two points on the hyperbola 2x2 $$-$$ y2 = 2. If ($$\alpha$$, $$\beta$$) is the point of the intersection of the normals to the hyperbola at A and B, then (2$$\beta$$)2 is equal to ____________.
2
JEE Main 2021 (Online) 27th August Morning Shift
Numerical
+4
-1
If the minimum area of the triangle formed by a tangent to the ellipse $${{{x^2}} \over {{b^2}}} + {{{y^2}} \over {4{a^2}}} = 1$$ and the co-ordinate axis is kab, then k is equal to _______________.
3
JEE Main 2021 (Online) 27th July Evening Shift
Numerical
+4
-1
Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its center at (3, $$-$$4), one focus at (4, $$-$$4) and one vertex at (5, $$-$$4). If mx $$-$$ y = 4, m > 0 is a tangent to the ellipse E, then the value of 5m2 is equal to _____________.
4
JEE Main 2021 (Online) 20th July Evening Shift
Numerical
+4
-1
If the point on the curve y2 = 6x, nearest to the point $$\left( {3,{3 \over 2}} \right)$$ is ($$\alpha$$, $$\beta$$), then 2($$\alpha$$ + $$\beta$$) is equal to _____________.
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